**Title: Understanding Power and Velocity in Physics****4. Power and Force in Motion**The power provided by a force can also be expressed as:\[ P = \frac{dW}{dt} = \mathbf{F} \cdot \mathbf{v} \]Where:- \( P \) is power,- \( dW/dt \) is the derivative of work with respect to time,- \( \mathbf{F} \) is the force vector,- \( \mathbf{v} \) is the velocity vector.**Given:**- A force \( \mathbf{F} = (3t\mathbf{i} - 2\mathbf{j} + 6\mathbf{k}) \, \text{N} \) is applied to an object. - The object is moving with a velocity \( \mathbf{v} = (2\mathbf{i} - 3t\mathbf{k}) \, \text{m/s} \).**a. Calculating Power and Effect on Speed**- **Objective:** Determine the power provided by this force and whether the object speeds up, slows down, or remains constant if this is the only unbalanced force acting on the object.**b. Perpendicular Force and Its Effects**- **Objective:** Consider a force that is always perpendicular to the velocity. Determine whether the object speeds up, slows down, or remains constant if this force is the only unbalanced force acting on the object.**Exploration:**For part (a), calculate the dot product of the force and velocity vectors to determine power and analyze the conditions under which the object's speed changes. For part (b), explore the implications of a force perpendicular to velocity, as such forces typically affect an object's direction rather than its speed.

4. The power provided by a force can also be written as P = dW/dt = F · dĩ/dt = F · v. A force F = (3t – 2j + 6k)N is applied to an object moving with a velocity v = (2î – 3k) m/s. a. What is the power provided by this force? Does the object speed up or slow down or neither, if this force is the only unbalanced force acting on the object? b. Consider a force that is always perpendicular to the velocity. Does the object speed up or slow down or neither, if this force is the only unbalanced force acting on the object?

4. The power provided by a force can also be written as P = dW/dt = F · dĩ/dt = F · v. A force F = (3t – 2j + 6k)N is applied to an object moving with a velocity v = (2î – 3k) m/s. a. What is the power provided by this force? Does the object speed up or slow down or neither, if this force is the only unbalanced force acting on the object? b. Consider a force that is always perpendicular to the velocity. Does the object speed up or slow down or neither, if this force is the only unbalanced force acting on the object?

Similar questions

Below is the potential energy diagram for a 50 gram particle. If the particle's mechanical energy is 7J: 10 U (1) 9 8 7 6 5 4 3 2 1 0 1 2 3 4 6 7 8 9 10 11 12 x (cm) A. Draw a line corresponding to the total Energy on the diagram. B. Assume the particle is moving in the positive x direction. Where is the particle speeding up? C. Assume the particle is moving in the positive x direction. Where is the particle lowing down? D. Where are any turning points in the particle's motion? E. What is the particle's speed at x=5 cm? F. What is the particle's maximum kinetic energy? Where does that occur? G. Suppose the particle's energy is decreased to 4J while the particle is between positions x = 7 cm and x = 9 cm. What is the particle's new maximum speed? Where does that occur?
1. A 66.1 kg runner has a speed of 4.70 m/s at one instant during a long-distance event. (a)What is the runner's kinetic energy at this instant (in J)? (b)How much net work (in J) is required to triple her speed?
Do not use Ug=mgh. Please
After pushing a 27.8 kg kid and tricycle over 8.2 m of smooth, level sidewalk from rest, the "combo" is moving at 3.8 m/s. Find the combo's kinetic energy. Submit Answer Tries 0/10 And, what net force must have been delivered to the combo? Submit Answer Tries 0/10 Now you stop pushing and let the combo coast to a stop. The only force stopping the combo is the force of friction. If the force of friction is 6.9 N, how far will the combo coast before it stops? Submit Answer Tries 0/10
ACTIVITY 1 Problem Solving Power Rating Power is the rate of doing work. Power depends on the amount of work done in a specific time. It is measure in joules/second or watts which is the SI unit. Horsepower often used in measuring power of machines but is not an SI unit. One horsepower is equivalent to 750 watts. Read, analyze, and solve the following problems using the GUFSA template. Show your complete solution. Round off your final answer to the nearest hundredths. 1. A piano mover pushes a piano with a force of 200 N, moving it 12 m in 15 s. With how much power does the piano mover need to push?
A crate with mass m = 33.3 kg being pushed up an incline that makes an angle φ = 22.7 degrees with horizontal. The pushing force is horizontal, with magnitude P, and the coefficient of kinetic friction between the crate and the incline is μ = 0.358. Consider the work done on the crate as it moves a distance d = 5.32 m at constant speed. a. What is work done by the pushing force, in joules? b. What is the work done by friction, in joules? c. What is the work done by gravity, in joules? d. What is the net work, in joules?
6. Please answer
39 A 1.00 kg block slides down a 20.0 meter ramp at a constant velocity. The angle of inclination of the ramp is 30°. How much work is done by friction? Ans. 98.0 J 45. A car pulls a trailer with a force of 2000 N at 20.0 m/s. What is the Ans. 4.00 x 104 Watts power exerted?
4. A 4.21-kg watermelon is released from rest from the roof of an 27.8-m-tall building. a. Calculate the work done by gravity on the watermelon as it falls from the roof to the ground. b. Calculate the net work done on the watermelon as it falls to the ground. Show clearly how you get your answer. Just before it hits the ground, what is the watermelon's kinetic energy? Show clearly how you get your answer. d. Just before it hits the ground, what is the watermelon's speed? (Use energy techniques to answer this.) C.
A freight elevator weighs 6200 N. What is the power required to raise the elevator a. What a distance of 20 meters in 10 seconds? b. One of the motors for the freight elevator system goes out. Now the maximum power available to move the 6200 N freight elevator is 10 kW. How long does it take to raise the elevator 20 meters now?
Suppose the object starts from rest, the slide is frictionless and m = 3.50 kg. (Neglect air drag) A. What is the speed of the mass at point B? B. What is the speed of the mass at point C? C. The work done by gravity on the mass as it moves from A to C?
An elevator is designed so that when it travels upward, it has constant acceleration from rest to its cruising speed of 2.0 m/s in a time of 4.0 seconds. The elevator has a mass of 625kg. Assume friction is ignored. A. Determine the average power (in W) of the elevator motor while its accelerating upward to its cruising speed. B. Determine the motor power (in W) when the elevator is moving upward at its cruising speed.